{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementation for Section 6\n",
    "\n",
    "**author: ** weiya<szcfweiya@gmail.com>\n",
    "\n",
    "**date: ** Dec. 28, 2017\n",
    "\n",
    "This notebook is to implement [the Section 6 in Chapter 11 of ESL](https://esl.hohoweiya.xyz/11%20Neural%20Networks/11.6%20Example%20of%20Simulated%20Data/index.html)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data\n",
    "$$\n",
    "Y=\\sigma(a_1^TX)+\\sigma(a_2^TX)+\\epsilon\n",
    "$$\n",
    "where $X^T=(X_1, X_2)$, and $X_j\\sim N(0,1)$. For the parameters, $a_1=(3,3),a_2=(3,-3)$. For the gaussian noise $\\epsilon$, we choose its variance to satisfy\n",
    "$$\n",
    "\\frac{Var(f(X))}{Var(\\epsilon)}=4\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.special import expit\n",
    "# set up\n",
    "num_train = 100\n",
    "num_test = 10000\n",
    "# generate X\n",
    "np.random.seed(123)\n",
    "X_train = np.random.normal(0, 1, (num_train, 2))\n",
    "X_test = np.random.normal(0, 1, (num_test, 2))\n",
    "# parameters\n",
    "a_1 = np.array([3, 3])\n",
    "a_2 = np.array([3, -3])\n",
    "epsi_var = np.var(X_train) / 4\n",
    "epsi_train = np.random.normal(0, np.sqrt(epsi_var), num_train)\n",
    "epsi_test = np.random.normal(0, np.sqrt(epsi_var), num_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# generate y\n",
    "y_train = expit(X_train.dot(a_1)) + expit(X_train.dot(a_2)) + epsi_train\n",
    "y_test = expit(X_test.dot(a_1)) + expit(X_test.dot(a_2)) + epsi_test\n",
    "y_train = y_train.reshape(num_train, 1)\n",
    "y_test = y_test.reshape(num_test, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prediction\n",
    "$$\n",
    "Z_m=\\sigma(\\alpha_{0m}+\\alpha_m^TX)\\qquad m=1,\\ldots, M\\\\\n",
    "T_k = \\beta_{0k}+\\beta_k^TZ\\qquad k=1,\\ldots,K\\\\\n",
    "f_k(X) = g_k(T) = T\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loss function\n",
    "$$\n",
    "R = \\sum\\limits_{i=1}^N\\sum\\limits_{k=1}^K(y_{ik}-f_k(x_i))^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BP\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{\\partial R_i}{\\partial \\beta_{km}}&=\\delta_{ki}z_{mi}\\\\\n",
    "\\frac{\\partial R_i}{\\partial \\alpha_{m\\ell}}&=s_{mi}x_{i\\ell}\\\\\n",
    "\\frac{\\partial R_i}{\\partial \\beta_{0k}}&=\\delta_{ki}\\\\\n",
    "\\frac{\\partial R_i}{\\partial \\alpha_{0m}}&=s_{mi}\n",
    "\\end{align}\n",
    "$$\n",
    "where\n",
    "$$\n",
    "s_{mi}=\\sigma'(\\alpha_{0m}+\\alpha_m^Tx_i)\\sum\\limits_{k=1}^K\\beta_{km}\\delta_{ki}\n",
    "$$\n",
    "$$\n",
    "\\delta_{ki}=-2(y_{ik}-f_k(x_i))g'_k(\\beta_{0k}+\\beta_k^Tz_i)\n",
    "$$\n",
    "and we have \n",
    "$$\n",
    "\\begin{align}\n",
    "\\sigma'(v)&=\\sigma(v)\\cdot(1-\\sigma(v))\\\\\n",
    "g_k'(T)&=1\n",
    "\\end{align}\n",
    "$$\n",
    "**Note:** for softmax function, we have $g_k'(T) = g_k(T)\\cdot (1-g_k(T)))$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def train_model(nn_hdim, num_passes = 5000, print_loss = False, reg_lambda = 0.0):\n",
    "    # initialize\n",
    "    # np.random.seed(123)\n",
    "    alpha = np.random.randn(2, nn_hdim) / np.sqrt(2)\n",
    "    a = np.zeros((1, nn_hdim))\n",
    "    beta = np.random.randn(nn_hdim, 1) / np.sqrt(nn_hdim)\n",
    "    b = np.zeros((1, 1))\n",
    "    \n",
    "    \n",
    "    gamma = 0.0005\n",
    "    \n",
    "    model = {}\n",
    "    \n",
    "    # gradient descent\n",
    "    for i in xrange(0, num_passes):\n",
    "        # forward pass\n",
    "        z = expit(X_train.dot(alpha) + a)\n",
    "        T = z.dot(beta) + b\n",
    "        pred = T\n",
    "        \n",
    "        # calculate the loss\n",
    "        if print_loss and i%100 == 0:\n",
    "            data_loss = np.sum(np.square(pred-y_train)) + reg_lambda/2 * (np.sum(np.square(alpha)) + np.sum(np.square(beta)))\n",
    "            print \"Loss after iteration %i: %f\" %(i, 1./num_train * data_loss)\n",
    "        \n",
    "        # back propagation\n",
    "        delta = -2*(y_train-pred)\n",
    "        dbeta = (z.T).dot(delta)\n",
    "        db = np.sum(delta, axis=0, keepdims=True)\n",
    "        s = delta.dot(beta.T) * (z*(1-z))\n",
    "        dalpha = np.dot(X_train.T, s)\n",
    "        da = np.sum(s, axis=0)\n",
    "        \n",
    "        # add regularization term\n",
    "        dbeta += reg_lambda * beta\n",
    "        dalpha += reg_lambda * alpha\n",
    "        \n",
    "        # gradient descent\n",
    "        alpha += -gamma * dalpha\n",
    "        a += -gamma * da\n",
    "        beta += -gamma * dbeta\n",
    "        b += -gamma * db\n",
    "        \n",
    "        # assign new parameters to the model\n",
    "        model = {'alpha': alpha, 'a': a, 'beta': beta, 'b':b}\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# test\n",
    "def test_model(model):\n",
    "    alpha, a, beta, b = model['alpha'], model['a'], model['beta'], model['b']\n",
    "    # forward pass\n",
    "    z = expit(X_test.dot(alpha) + a)\n",
    "    T = z.dot(beta) + b\n",
    "    pred = T\n",
    "    pred_loss = 1./num_test * np.sum(np.square(pred-y_test)) \n",
    "    return pred_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# vary the number of hidden units\n",
    "num_cases = 10\n",
    "num_repeat = 10\n",
    "mat_loss = np.zeros((num_repeat, num_cases))\n",
    "for i in xrange(0, 10):\n",
    "    for j in xrange(0, num_repeat):\n",
    "        model = train_model(i+1)\n",
    "        mat_loss[j, i] = test_model(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The Bayes rate for regression with squared error is the error variance.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Yo9tzZmT7AkwkrfnzODA2GzueNFNyPLA68AIwFTiqv2DGj4dXXklFseuvn/OIzMzMLJea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\n/gVeuaD30WptzgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f406cea2150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([x+1 for x in range(10)], mat_loss.mean(axis=0)/epsi_var)\n",
    "plt.ylabel('test error (relative to the Bayes error)')\n",
    "plt.xlabel('number of hidden units')\n",
    "plt.title('sum of sigmoids')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZLVMlzQAejYh7JZ0GbBYRh5ecMyOrvwGwcfZ+RUQMLb91GTBH0l+AP5BWWT0FmD8el3g3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\nGYOHJElqxuAhSZKa+Q2ISyc41t6MIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f406d254a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# boxplot\n",
    "plt.boxplot(mat_loss/epsi_var)\n",
    "plt.ylabel('test error (relative to the Bayes error)')\n",
    "plt.xlabel('number of hidden units')\n",
    "plt.title('sum of sigmoids')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# weight decay\n",
    "# vary the number of hidden units\n",
    "mat_loss_reg = np.zeros((num_repeat, num_cases))\n",
    "for i in xrange(0, 10):\n",
    "    for j in xrange(0, num_repeat):\n",
    "        model = train_model(i+1, reg_lambda=0.1)\n",
    "        mat_loss_reg[j, i] = test_model(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6APGbmZlZBXJ1LpX0ZeA/SZNzLV34WERU3TkiIm6hlxE2EbFfibI+R+RExN9J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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f406cd90190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# boxplot\n",
    "plt.boxplot(mat_loss_reg/epsi_var)\n",
    "plt.ylabel('test error (relative to the Bayes error)')\n",
    "plt.xlabel('number of hidden units')\n",
    "plt.title('sum of sigmoids (weight decay = 0.1)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# vary the rate of weight decay\n",
    "seq_lambda = np.arange(0.0, 0.2, 0.02)\n",
    "mat_loss_vary_lambda = np.zeros((num_repeat, len(seq_lambda)))\n",
    "for i in xrange(0, len(seq_lambda)):\n",
    "    for j in xrange(0, num_repeat):\n",
    "        model = train_model(10, reg_lambda=seq_lambda[i])\n",
    "        mat_loss_vary_lambda[j, i] = test_model(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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L8Ks8/AU+vt18M2y9dXP7zG2yX8VNNzn5MGtWrsRD0quBQ4AtgLdHxN8kvQe4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f406d4ea510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# boxplot\n",
    "plt.boxplot(mat_loss_vary_lambda/epsi_var)\n",
    "plt.ylabel('test error (relative to the Bayes error)')\n",
    "plt.xlabel('weight decay rate')\n",
    "plt.xticks([x+1 for x in range(10)], seq_lambda)\n",
    "plt.title('sum of sigmoids (10 hidden units)')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:anaconda2]",
   "language": "python",
   "name": "conda-env-anaconda2-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
